In compound adjectives like “unique Son” (μονογενής) the -γενής suggests deriviation in general rather than birth. 

Murray Harris在他的Jesus as God一書中的詞源學研究

Etymologically, therefore, the term (μονογενής) “is not associated with begetting (γεννᾶσθαι) but with existence (γίγνεσθαι).”